MATH (MATH) for graduation. Prereq: MATH 121, MATH 123 or MATH 125.
|
|
- Scot Wood
- 6 years ago
- Views:
Transcription
1 MATH (MATH) 1 MATH (MATH) MATH 120. Elementary Functions and Analytic Geometry. 3 Units. Polynomial, rational, exponential, logarithmic, and trigonometric functions (emphasis on computation, graphing, and location of roots) straight lines and conic sections. Primarily a precalculus course for the student without a good background in trigonometric functions and graphing and/ or analytic geometry. Not open to students with credit for MATH 121 or MATH 125. Prereq: Three years of high school mathematics. MATH 121. Calculus for Science and Engineering I. 4 Units. Functions, analytic geometry of lines and polynomials, limits, derivatives of algebraic and trigonometric functions. Definite integral, antiderivatives, fundamental theorem of calculus, change of variables. Recommended preparation: Three and one half years of high school mathematics. Credit for at most one of MATH 121, MATH 123 and MATH 125 can be applied to hours required for graduation. Counts for CAS Quantitative Reasoning Requirement. Prereq: MATH 120 or a score of 25 on the mathematics diagnostic test. MATH 122. Calculus for Science and Engineering II. 4 Units. Continuation of MATH 121. Exponentials and logarithms, growth and decay, inverse trigonometric functions, related rates, basic techniques of integration, area and volume, polar coordinates, parametric equations. Taylor polynomials and Taylor's theorem. Credit for at most one of MATH 122, MATH 124, and MATH 126 can be applied to hours required for graduation. Prereq: MATH 121, MATH 123 or MATH 126. MATH 123. Calculus I. 4 Units. Limits, continuity, derivatives of algebraic and transcendental functions, including applications, basic properties of integration. Techniques of integration and applications. Students must have 31/2 years of high school mathematics. Credit for at most one of MATH 121, MATH 123, and MATH 125 can be applied to hours required for graduation. Counts for CAS Quantitative Reasoning Requirement. MATH 124. Calculus II. 4 Units. Review of differentiation. Techniques of integration, and applications of the definite integral. Parametric equations and polar coordinates. Taylor's theorem. Sequences, series, power series. Complex arithmetic. Introduction to multivariable calculus. Credit for at most one of MATH 122, MATH 124, and MATH 126 can be applied to hours required for graduation. Prereq: MATH 121 and placement by department. MATH 125. Math and Calculus Applications for Life, Managerial, and Social Sci I. 4 Units. Discrete and continuous probability; differential and integral calculus of one variable; graphing, related rates, maxima and minima. Integration techniques, numerical methods, volumes, areas. Applications to the physical, life, and social sciences. Students planning to take more than two semesters of introductory mathematics should take MATH 121. Recommended preparation: Three and one half years of high school mathematics. Credit for at most one of MATH 121, MATH 123, and MATH 125 can be applied to hours required for graduation. Counts for CAS Quantitative Reasoning Requirement. Prereq: MATH 120 or a score of 25 or above on the mathematics diagnostic exam. MATH 126. Math and Calculus Applications for Life, Managerial, and Social Sci II. 4 Units. Continuation of MATH 125 covering differential equations, multivariable calculus, discrete methods. Partial derivatives, maxima and minima for functions of two variables, linear regression. Differential equations; first and second order equations, systems, Taylor series methods; Newton's method; difference equations. Credit for at most one of MATH 122, MATH 124, and MATH 126 can be applied to hours required for graduation. Prereq: MATH 121, MATH 123 or MATH 125. MATH 150. Mathematics from a Mathematician's Perspective. 3 Units. An interesting and accessible mathematical topic not covered in the standard curriculum is developed. Students are exposed to methods of mathematical reasoning and historical progression of mathematical concepts. Introduction to the way mathematicians work and their attitude toward their profession. Should be taken in freshman year to count toward a major in mathematics. Prereq: Three and one half years of high school mathematics. Counts for CAS Quantitative Reasoning Requirement. MATH 201. Introduction to Linear Algebra for Applications. 3 Units. Matrix operations, systems of linear equations, vector spaces, subspaces, bases and linear independence, eigenvalues and eigenvectors, diagonalization of matrices, linear transformations, determinants. Less theoretical than MATH 307. Appropriate for majors in science, engineering, economics. Prereq: MATH 122, MATH 124 or MATH 126. MATH 223. Calculus for Science and Engineering III. 3 Units. Introduction to vector algebra; lines and planes. Functions of several variables: partial derivatives, gradients, chain rule, directional derivative, maxima/minima. Multiple integrals, cylindrical and spherical coordinates. Derivatives of vector valued functions, velocity and acceleration. Vector fields, line integrals, Green's theorem. Credit for at most one of MATH 223 and MATH 227 can be applied to hours required for graduation. Prereq: MATH 122 or MATH 124. MATH 224. Elementary Differential Equations. 3 Units. A first course in ordinary differential equations. First order equations and applications, linear equations with constant coefficients, linear systems, Laplace transforms, numerical methods of solution. Credit for at most one of MATH 224 and MATH 228 can be applied to hours required for graduation. Prereq: MATH 223 or MATH 227. MATH 227. Calculus III. 3 Units. Vector algebra and geometry. Linear maps and matrices. Calculus of vector valued functions. Derivatives of functions of several variables. Multiple integrals. Vector fields and line integrals. Credit for at most one of MATH 223 and MATH 227 can be applied to hours required for graduation. Prereq: MATH 124 and placement by the department. MATH 228. Differential Equations. 3 Units. Elementary ordinary differential equations: first order equations; linear systems; applications; numerical methods of solution. Credit for at most one of MATH 224 and MATH 228 can be applied to hours required for graduation. Prereq: MATH 227 or placement by the department. MATH 301. Undergraduate Reading Course. 1-3 Units. Students must obtain the approval of a supervising professor before registration. More than one credit hour must be approved by the undergraduate committee of the department.
2 2 MATH (MATH) MATH 302. Departmental Seminar. 3 Units. A seminar devoted to understanding the formulation and solution of mathematical problems. SAGES Department Seminar. Students will investigate, from different possible viewpoints, via case studies, how mathematics advances as a discipline--what mathematicians do. The course will largely be in a seminar format. There will be two assignments involving writing in the style of the discipline. Enrollment by permission (limited to majors depending on demand). Counts as SAGES Departmental Seminar. MATH 303. Elementary Number Theory. 3 Units. Primes and divisibility, theory of congruencies, and number theoretic functions. Diophantine equations, quadratic residue theory, and other topics determined by student interest. Emphasis on problem solving (formulating conjectures and justifying them). Prereq: MATH 122 or MATH 124. MATH 304. Discrete Mathematics. 3 Units. A general introduction to basic mathematical terminology and the techniques of abstract mathematics in the context of discrete mathematics. Topics introduced are mathematical reasoning, Boolean connectives, deduction, mathematical induction, sets, functions and relations, algorithms, graphs, combinatorial reasoning. Offered as EECS 302 and MATH 304. Prereq: MATH 122, MATH 124 or MATH 126. MATH 305. Introduction to Advanced Mathematics. 3 Units. A course on the theory and practice of writing, and reading mathematics. Main topics are logic and the language of mathematics, proof techniques, set theory, and functions. Additional topics may include introductions to number theory, group theory, topology, or other areas of advanced mathematics. Prereq: MATH 122, MATH 124 or MATH 126. MATH 307. Linear Algebra. 3 Units. A course in linear algebra that studies the fundamentals of vector spaces, inner product spaces, and linear transformations on an axiomatic basis. Topics include: solutions of linear systems, matrix algebra over the real and complex numbers, linear independence, bases and dimension, eigenvalues and eigenvectors, singular value decomposition, and determinants. Other topics may include least squares, general inner product and normed spaces, orthogonal projections, finite dimensional spectral theorem. This course is required of all students majoring in mathematics and applied mathematics. More theoretical than MATH 201. Prereq: MATH 122 or MATH 124. MATH 308. Introduction to Abstract Algebra. 3 Units. A first course in abstract algebra, studied on an axiomatic basis. The major algebraic structures studied are groups, rings and fields. Topics include homomorphisms and quotient structures. This course is required of all students majoring in mathematics. It is helpful, but not necessary, for a student to have taken MATH 307 before MATH 308. Prereq: MATH 122 or MATH 124. MATH 319. Applied Probability and Stochastic Processes for Biology. 3 Units. Applications of probability and stochastic processes to biological systems. Mathematical topics will include: introduction to discrete and continuous probability spaces (including numerical generation of pseudo random samples from specified probability distributions), Markov processes in discrete and continuous time with discrete and continuous sample spaces, point processes including homogeneous and inhomogeneous Poisson processes and Markov chains on graphs, and diffusion processes including Brownian motion and the Ornstein- Uhlenbeck process. Biological topics will be determined by the interests of the students and the instructor. Likely topics include: stochastic ion channels, molecular motors and stochastic ratchets, actin and tubulin polymerization, random walk models for neural spike trains, bacterial chemotaxis, signaling and genetic regulatory networks, and stochastic predator-prey dynamics. The emphasis will be on practical simulation and analysis of stochastic phenomena in biological systems. Numerical methods will be developed using a combination of MATLAB, the R statistical package, MCell, and/or URDME, at the discretion of the instructor. Student projects will comprise a major part of the course. Offered as BIOL 319, EECS 319, MATH 319, SYBB 319, BIOL 419, EBME 419, MATH 419, PHOL 419, and SYBB 419. Prereq: MATH 224 or MATH 223 and BIOL 300 or BIOL 306 and MATH 201 or MATH 307 or consent of instructor. MATH 321. Fundamentals of Analysis I. 3 Units. Abstract mathematical reasoning in the context of analysis in Euclidean space. Introduction to formal reasoning, sets and functions, and the number systems. Sequences and series; Cauchy sequences and convergence. Required for all mathematics majors. Additional work required for graduate students. (May not be taken for graduate credit by graduate students in the Department of Mathematics.) Offered as MATH 321 and MATH 421. Prereq: MATH 223 or MATH 227. MATH 322. Fundamentals of Analysis II. 3 Units. Continuation of MATH 321. Point-set topology in metric spaces with attention to n-dimensional space; completeness, compactness, connectedness, and continuity of functions. Topics in sequences, series of functions, uniform convergence, Fourier series and polynomial approximation. Theoretical development of differentiation and Riemann integration. Required for all mathematics majors. Additional work required for graduate students. (May not be taken for graduate credit by graduate students in the Department of Mathematics.) Offered as MATH 322 and MATH 422. Prereq: MATH 321. MATH 324. Introduction to Complex Analysis. 3 Units. Properties, singularities, and representations of analytic functions, complex integration. Cauchy's theorems, series residues, conformal mapping and analytic continuation. Riemann surfaces. Relevance to the theory of physical problems. Prereq: MATH 224 or MATH 228. MATH 327. Convexity and Optimization. 3 Units. Introduction to the theory of convex sets and functions and to the extremes in problems in areas of mathematics where convexity plays a role. Among the topics discussed are basic properties of convex sets (extreme points, facial structure of polytopes), separation theorems, duality and polars, properties of convex functions, minima and maxima of convex functions over convex set, various optimization problems. Offered as MATH 327, MATH 427, and OPRE 427. Prereq: MATH 223 or MATH 227.
3 MATH (MATH) 3 MATH 330. Introduction of Scientific Computing. 3 Units. An introductory survey to Scientific Computing from principles to applications. Topics which will be covered in the course include: solution of linear systems and least squares, approximation and interpolation, solution of nonlinear systems, numerical integration and differentiation, and numerical solution of differential equations. Projects where the numerical methods are used to solve problems from various application areas will be assigned throughout the semester. Prereq: MATH 224 or MATH 228. MATH 333. Mathematics and Brain. 3 Units. This course is intended for upper level undergraduate students in Mathematics, Cognitive Science, Biomedical Engineering, Biology or Neuroscience who have an interest in quantitative investigation of the brain and its functions. Students will be introduced to a variety of mathematical techniques needed to model and simulate different brain functions, and to analyze the results of the simulations and of available measured data. The mathematical exposition will be followed--when appropriate--by the corresponding implementation in Matlab. The course will cover some basic topics in the mathematical aspects of differential equations, electromagnetism, Inverse problems and imaging related to brain functions. Validation and falsification of the mathematical models in the light of available experimental data will be addressed. This course will be a first step towards organizing the different brain investigative modalities within a unified mathematical framework. Lectures will include a discussion portion. A final presentation and written report are part of the course requirements. Counts as SAGES Departmental Seminar. Prereq: MATH 224 or MATH 228. MATH 338. Introduction to Dynamical Systems. 3 Units. Nonlinear discrete dynamical systems in one and two dimensions. Chaotic dynamics, elementary bifurcation theory, hyperbolicity, symbolic dynamics, structural stability, stable manifold theory. Prereq: MATH 223 or MATH 227. MATH 343. Theoretical Computer Science. 3 Units. Introduction to different classes of automata and their correspondence to different classes of formal languages and grammars, computability, complexity and various proof techniques. Offered as EECS 343 and MATH 343. Prereq: MATH 304 and EECS 340. MATH 351. Senior Project for the Mathematics and Physics Program. 2 Units. A two-semester course (2 credits per semester) in the joint B.S. in Mathematics and Physics program. Project based on numerical and/ or theoretical research under the supervision of a mathematics faculty member, possibly jointly with a faculty member from physics. Study of the techniques utilized in a specific research area and of recent literature associated with the project. Work leading to meaningful results which are to be presented as a term paper and an oral report at the end of the second semester. Supervising faculty will review progress with the student on a regular basis, including detailed progress reports made twice each semester, to ensure successful completion of the work. Counts as SAGES Senior Capstone. MATH 352. Mathematics Capstone. 3 Units. Mathematics Senior Project. Students pursue a project based on experimental, theoretical or teaching research under the supervision of a mathematics faculty member, a faculty member from another Case department or a research scientist or engineer from another institution. A departmental Senior Project Coordinator must approve all project proposals and this same person will receive regular oral and written progress reports. Final results are presented at the end of the second semester as a paper in a style suitable for publication in a professional journal as well as an oral report in a public Mathematics Capstone symposium. Counts as SAGES Senior Capstone. MATH 357. Mathematical Modeling Across the Sciences. 3 Units. A three credit course on mathematical modeling as it applies to the origins sciences. Students gain practical experience in a wide range of techniques for modeling research questions in cosmology and astrophysics, integrative evolutionary biology (including physical anthropology, ecology, paleontology, and evolutionary cognitive science), and planetary science and astrobiology. Offered as ORIG 301, ORIG 401 and MATH 357. Prereq: ORIG 201, ORIG 202, BIOL 225, MATH 122, CHEM 106 and (PHYS 122 or PHYS 124). MATH 361. Geometry I. 3 Units. An introduction to the various two-dimensional geometries, including Euclidean, spherical, hyperbolic, projective, and affine. The course will examine the axiomatic basis of geometry, with an emphasis on transformations. Topics include the parallel postulate and its alternatives, isometrics and transformation groups, tilings, the hyperbolic plane and its models, spherical geometry, affine and projective transformations, and other topics. We will examine the role of complex and hypercomplex numbers in the algebraic representation of transformations. The course is self-contained. Counts as SAGES Departmental Seminar. Prereq: MATH 224. MATH 363. Knot Theory. 3 Units. An introduction to the mathematical theory of knots and links, with emphasis on the modern combinatorial methods. Reidemeister moves on link projections, ambient and regular isotopies, linking number tricolorability, rational tangles, braids, torus knots, seifert surfaces and genus, the knot polynomials (bracket, X, Jones, Alexander, HOMFLY), crossing numbers of alternating knots and amphicheirality. Connections to theoretical physics, molecular biology, and other scientific applications will be pursued in term projects, as appropriate to the background and interests of the students. Prereq: MATH 223 or MATH 227. MATH 365. Introduction To Algebraic Geometry. 3 Units. This is a first introduction to algebraic geometry - the study of solutions of polynomial equations - for advanced undergraduate students. Recent applications of this large and important area include number theory, combinatorics, theoretical physics, coding theory, and robotics. In this course we will learn the basic objects and notions of algebraic geometry. Topics that are planned to be covered are affine and projective varieties, the Zariski topology, the correspondence between ideals and varieties, the sheaf of regular functions, regular and rational maps, dimensions and tangent spaces. Examples such as Grassmannians, curves, and blowups will be discussed. Depending on time constraints, we may also touch upon the modern language of schemes, line bundles and the Riemann Roch formula, and algorithmic techniques such as Groebner bases. Prereq: MATH 307 and Coreq: MATH 308.
4 4 MATH (MATH) MATH 376. Mathematical Analysis of Biological Models. 3 Units. This course focuses on the mathematical methods used to analyze biological models, with examples drawn largely from ecology but also from epidemiology, developmental biology, and other areas. Mathematical topics include equilibrium and stability in discrete and continuous time, some aspects of transient dynamics, and reaction-diffusion equations (steady state, diffusive instabilities, and traveling waves). Biological topics include several "classic" models, such as the Lotka-Volterra model, the Ricker model, and Michaelis-Menten/type II/saturating responses. The emphasis is on approximations that lead to analytic solutions, not numerical analysis. An important aspect of this course is translating between verbal and mathematical descriptions: the goal is not just to solve mathematical problems but to extract biological meaning from the answers we find. Offered as BIOL 306 and MATH 376. Prereq: BIOL 300 or MATH 224 or consent of instructor. MATH 378. Computational Neuroscience. 3 Units. Computer simulations and mathematical analysis of neurons and neural circuits, and the computational properties of nervous systems. Students are taught a range of models for neurons and neural circuits, and are asked to implement and explore the computational and dynamic properties of these models. The course introduces students to dynamical systems theory for the analysis of neurons and neural learning, models of brain systems, and their relationship to artificial and neural networks. Term project required. Students enrolled in MATH 478 will make arrangements with the instructor to attend additional lectures and complete additional assignments addressing mathematical topics related to the course. Recommended preparation: MATH 223 and MATH 224 or BIOL 300 and BIOL 306. Offered as BIOL 378, COGS 378, MATH 378, BIOL 478, EBME 478, EECS 478, MATH 478 and NEUR 478. MATH 380. Introduction to Probability. 3 Units. Combinatorial analysis. Permutations and combinations. Axioms of probability. Sample space and events. Equally likely outcomes. Conditional probability. Bayes' formula. Independent events and trials. Discrete random variables, probability mass functions. Expected value, variance. Bernoulli, binomial, Poisson, geometric, negative binomial random variables. Continuous random variables, density functions. Expected value and variance. Uniform, normal, exponential, Gamma random variables. The De Moivre-Laplace limit theorem. Joint probability mass functions and densities. Independent random variables and the distribution of their sums. Covariance. Conditional expectations and distributions (discrete case). Moment generating functions. Law of large numbers. Central limit theorem. Additional topics (time permitting): the Poisson process, finite state space Markov chains, entropy. Prereq: MATH 223 or MATH 227. MATH 383. Topics in Probability. 3 Units. This is a second undergraduate course in probability. Topics may include: Stochastic processes, Markov chains, Brownian motion, martingales, measure-theoretic foundations of probability, quantitative limit theory/ rates of convergence, coupling methods, Fourier methods, and ergodic theory. Prereq: MATH 380. MATH 394. Introduction to Information Theory. 3 Units. This course is intended as an introduction to information and coding theory with emphasis on the mathematical aspects. It is suitable for advanced undergraduate and graduate students in mathematics, applied mathematics, statistics, physics, computer science and electrical engineering. Course content: Information measures-entropy, relative entropy, mutual information, and their properties. Typical sets and sequences, asymptotic equipartition property, data compression. Channel coding and capacity: channel coding theorem. Differential entropy, Gaussian channel, Shannon-Nyquist theorem. Information theory inequalities (400 level). Additional topics, which may include compressed sensing and elements of quantum information theory. Recommended preparation: MATH 201 or MATH 307. Offered as MATH 394, EECS 394, MATH 494 and EECS 494. Prereq: MATH 223 and MATH 380 or requisites not met permission. MATH 400. Mathematics Teaching Practicum. 1 Unit. Practicum for teaching college mathematics. Includes preparation of syllabi, exams, lectures. Grading, alternative teaching styles, use of technology, interpersonal relations and motivation. Handling common problems and conflicts. MATH 401. Abstract Algebra I. 3 Units. Basic properties of groups, rings, modules and fields. Isomorphism theorems for groups; Sylow theorem; nilpotency and solvability of groups; Jordan-Holder theorem; Gauss lemma and Eisenstein's criterion; finitely generated modules over principal ideal domains with applications to abelian groups and canonical forms for matrices; categories and functors; tensor product of modules, bilinear and quadratic forms; field extensions; fundamental theorem of Galois theory, solving equations by radicals. Prereq: MATH 308. MATH 402. Abstract Algebra II. 3 Units. A continuation of MATH 401. Prereq: MATH 401. MATH 405. Advanced Matrix Analysis. 3 Units. An advanced course in linear algebra and matrix theory. Topics include variational characterizations of eigenvalues of Hermitian matrices, matrix and vector norms, characterizations of positive definite matrices, singular value decomposition and applications, perturbation of eigenvalues. This course is more theoretical than MATH 431, which emphasizes computational aspects of linear algebra Prereq: MATH 307. MATH 406. Mathematical Logic and Model Theory. 3 Units. Propositional calculus and quantification theory; consistency and completeness theorems; Gödel incompleteness results and their philosophical significance; introduction to basic concepts of model theory; problems of formulation of arguments in philosophy and the sciences. Offered as PHIL 306, MATH 406 and PHIL 406. MATH 408. Introduction to Cryptology. 3 Units. Introduction to the mathematical theory of secure communication. Topics include: classical cryptographic systems; one-way and trapdoor functions; RSA, DSA, and other public key systems; Primality and Factorization algorithms; birthday problem and other attack methods; elliptic curve cryptosystems; introduction to complexity theory; other topics as time permits. Recommended preparation: MATH 303. MATH 413. Graph Theory. 3 Units. Building blocks of a graph, trees, connectivity, matchings, coverings, planarity, NP-complete problems, random graphs, and expander graphs; various applications and algorithms. Prereq: MATH 201 or MATH 307.
5 MATH (MATH) 5 MATH 419. Applied Probability and Stochastic Processes for Biology. 3 Units. Applications of probability and stochastic processes to biological systems. Mathematical topics will include: introduction to discrete and continuous probability spaces (including numerical generation of pseudo random samples from specified probability distributions), Markov processes in discrete and continuous time with discrete and continuous sample spaces, point processes including homogeneous and inhomogeneous Poisson processes and Markov chains on graphs, and diffusion processes including Brownian motion and the Ornstein- Uhlenbeck process. Biological topics will be determined by the interests of the students and the instructor. Likely topics include: stochastic ion channels, molecular motors and stochastic ratchets, actin and tubulin polymerization, random walk models for neural spike trains, bacterial chemotaxis, signaling and genetic regulatory networks, and stochastic predator-prey dynamics. The emphasis will be on practical simulation and analysis of stochastic phenomena in biological systems. Numerical methods will be developed using a combination of MATLAB, the R statistical package, MCell, and/or URDME, at the discretion of the instructor. Student projects will comprise a major part of the course. Offered as BIOL 319, EECS 319, MATH 319, SYBB 319, BIOL 419, EBME 419, MATH 419, PHOL 419, and SYBB 419. MATH 421. Fundamentals of Analysis I. 3 Units. Abstract mathematical reasoning in the context of analysis in Euclidean space. Introduction to formal reasoning, sets and functions, and the number systems. Sequences and series; Cauchy sequences and convergence. Required for all mathematics majors. Additional work required for graduate students. (May not be taken for graduate credit by graduate students in the Department of Mathematics.) Offered as MATH 321 and MATH 421. MATH 422. Fundamentals of Analysis II. 3 Units. Continuation of MATH 321. Point-set topology in metric spaces with attention to n-dimensional space; completeness, compactness, connectedness, and continuity of functions. Topics in sequences, series of functions, uniform convergence, Fourier series and polynomial approximation. Theoretical development of differentiation and Riemann integration. Required for all mathematics majors. Additional work required for graduate students. (May not be taken for graduate credit by graduate students in the Department of Mathematics.) Offered as MATH 322 and MATH 422. Prereq: MATH 321 or MATH 421. MATH 423. Introduction to Real Analysis I. 3 Units. General theory of measure and integration. Measures and outer measures. Lebesgue measure on n-space. Integration. Convergence theorems. Product measures and Fubini's theorem. Signed measures. Hahn-Jordan decomposition, Radon-Nikodym theorem, and Lebesgue decomposition. SpaceP-integrable function. Lebesgue differentiation theorem in n-space. Prereq: MATH 322 or MATH 422. MATH 424. Introduction to Real Analysis II. 3 Units. Measures on locally compact spaces. Riesz representation theorem. Elements of functional analysis. Normed linear spaces. Hahn-Banach, Banach-Steinhaus, open mapping, closed graph theorems. Weak topologies. Banach-Alaoglu theorem. Function spaces. Stone-Weierstrass and Ascoli theorems. Basic Hilbert space theory. Application to Fourier series. Additional topics: Haar measure on locally compact groups. Prereq: MATH 423. MATH 425. Complex Analysis I. 3 Units. Analytic functions. Integration over paths in the complex plane. Index of a point with respect to a closed path; Cauchy's theorem and Cauchy's integral formula; power series representation; open mapping theorem; singularities; Laurent expansion; residue calculus; harmonic functions; Poisson's formula; Riemann mapping theorem. More theoretical and at a higher level than MATH 324. Prereq: MATH 322 or MATH 422. MATH 427. Convexity and Optimization. 3 Units. Introduction to the theory of convex sets and functions and to the extremes in problems in areas of mathematics where convexity plays a role. Among the topics discussed are basic properties of convex sets (extreme points, facial structure of polytopes), separation theorems, duality and polars, properties of convex functions, minima and maxima of convex functions over convex set, various optimization problems. Offered as MATH 327, MATH 427, and OPRE 427. MATH 431. Introduction to Numerical Analysis I. 3 Units. Numerical linear algebra for scientists and engineers. Matrix and vector norms, computer arithmetic, conditioning and stability, orthogonality. Least squares problems: QR factorization, normal equations and Singular Value Decomposition. Direct solution of linear system: Gaussian elimination and Cholesky factorization. Eigenvalues and eigenvectors: the QR algorithm, Rayleigh quotient, inverse iteration. Introduction to iterative methods. Students will be introduced to MATLAB. Prereq: MATH 201 or MATH 307. MATH 432. Numerical Differential Equations. 3 Units. Numerical solution of differential equations for scientists and engineers. Solution of ordinary differential equations by multistep and single step methods. Stability, consistency, and convergence. Stiff equations. Finite difference schemes. Introduction to the finite element method. Introduction to multigrid techniques. The diffusion equation: numerical schemes and stability analysis. Introduction to hyperbolic equations. MATLAB will be used in this course. Prereq: MATH 224 or MATH 228. MATH 433. Numerical Solutions of Nonlinear Systems and Optimization. 3 Units. The course provides an introduction to numerical solution methods for systems of nonlinear equations and optimization problems. The course is suitable for upper-undergraduate and graduate students with some background in calculus and linear algebra. Knowledge of numerical linear algebra is helpful. Among the topics which will be covered in the course are Nonlinear systems in one variables; Newton's method for nonlinear equations and unconstrained minimization; Quasi-Newton methods; Global convergence of Newton's methods and line searches; Trust region approach; Secant methods; Nonlinear least squares. Prereq: MATH 223 or MATH 227, and MATH 431 or permission. MATH 434. Optimization of Dynamic Systems. 3 Units. Fundamentals of dynamic optimization with applications to control. Variational treatment of control problems and the Maximum Principle. Structures of optimal systems; regulators, terminal controllers, timeoptimal controllers. Sufficient conditions for optimality. Singular controls. Computational aspects. Selected applications. Recommended preparation: EECS 408. Offered as EECS 421 and MATH 434.
6 6 MATH (MATH) MATH 435. Ordinary Differential Equations. 3 Units. A second course in ordinary differential equations. Existence, uniqueness, and continuation of solutions of ODE. Linear systems, fundamental matrix, qualitative methods (phase plane). Dependence on initial data and parameters (Gronwall's inequality, nonlinear variation of parameters). Stability for linear and nonlinear equations, linearization, Poincare- Bendixson theory. Additional topics may include regular and singular perturbation methods, autonomous oscillations, entrainment of forced oscillators, and bifurcations. Prereq: MATH 224 and either MATH 201 or MATH 307. MATH 439. Integrated Numerical and Statistical Computations. 3 Units. This course will embed numerical methods into a Bayesian framework. The statistical framework will make it possible to integrate a prori information about the unknowns and the error in the data directly into the most efficient numerical methods. A lot of emphasis will be put on understanding the role of the priors, their encoding into fast numerical solvers, and how to translate qualitative or sample-based information--or lack thereof--into a numerical scheme. Confidence on computed results will also be discussed from a Bayesian perspective, at the light of the given data and a priori information. The course should be of interest to anyone working on signal and image processing statistics, numerical analysis and modeling. Recommended Preparation: MATH 431. Offered as MATH 439 and STAT 439. MATH 440. Computational Inverse Problems. 3 Units. This course will introduce various computational methods for solving inverse problems under different conditions. First the classical regularization methods will be introduced, and the computational challenges which they pose, will be addressed. Following this, the statistical methods for solving inverse problems will be studied and their computer implementation discussed. We will combine the two approaches to best exploit their potentials. Applications arising from various areas of science, engineering, and medicine will be discussed throughout the course. MATH 441. Mathematical Modeling. 3 Units. Mathematics is a powerful language for describing real world phenomena and providing predictions that otherwise are hard or impossible to obtain. The course gives the students pre-requisites for translating qualitative descriptions given in the professional non-mathematical language into the quantitative language for mathematics. While the variety in the subject matter is wide, some general principles and methodologies that a modeler can pursue are similar in many applications. The course focuses on these similarities. The course is based on representative case studies that are discussed and analyzed in the classroom, the emphasis being on general principles of developing and analyzing mathematical models. The examples will be taken from different fields of science and engineering, including life sciences, environmental sciences, biomedical engineering and physical sciences. Modeling relies increasingly on computation, so the students should have basic skills for using computers and programs like Matlab or Mathematica. Prereq: MATH 224 or MATH 228. MATH 444. Mathematics of Data Mining and Pattern Recognition. 3 Units. This course will give an introduction to a class of mathematical and computational methods for the solution of data mining and pattern recognition problems. By understanding the mathematical concepts behind algorithms designed for mining data and identifying patterns, students will be able to modify to make them suitable for specific applications. Particular emphasis will be given to matrix factorization techniques. The course requirements will include the implementations of the methods in MATLAB and their application to practical problems. Prereq: MATH 201 or MATH 307. MATH 445. Introduction to Partial Differential Equations. 3 Units. Method of characteristics for linear and quasilinear equations. Second order equations of elliptic, parabolic, type; initial and boundary value problems. Method of separation of variables, eigenfunction expansions, Sturm-Liouville theory. Fourier, Laplace, Hankel transforms; Bessel functions, Legendre polynomials. Green's functions. Examples include: heat diffusion, Laplace's equation, wave equations, one dimensional gas dynamics and others. Appropriate for seniors and graduate students in science, engineering, and mathematics. Prereq: MATH 201 or MATH 307 and MATH 224 or MATH 228. MATH 446. Numerical Methods for Partial Differential Equations. 3 Units. This course is an introduction to numerical methods of PDEs, and in particular, to finite element methods (FEM), emphasizing the interconnection between the functional analytic viewpoint of PDEs and the practical and effective computation of the numerical approximations. In particular, the emphasis is on showing that many of the useful and elegant ideas in finite dimensional linear algebra have a natural counterpart in the infinite dimensional setting of Hilbert spaces, and that the same techniques that guarantee the existence and uniqueness of the solutions in fact provide also stable computational methods to approximate the solutions. The topics covered in this course include Fourier analysis, weak derivatives, weak forms, generalized functions; Sobolev spaces, trace theorem, compact embedding theorems, Poincare inequalities; Riesz theory, Fredholm theory; Finite Element Method (FEM): Grid generation, existence, stability and convergence of solutions for elliptic problems; Semi-discretization of parabolic and hyperbolic equations; Stiffness; Numerical solution of linear systems by iterative methods. A quintessential part of this course comprises numerical implementation of the finite element method. Matlab is used as the programming tool both in demonstrations and examples in the class as well as in home assignments. Recommended Preparation: linear algebra, multivariate calculus, and ordinary differential equations. MATH 449. Dynamical Models for Biology and Medicine. 3 Units. Introduction to discrete and continuous dynamical models with applications to biology and medicine. Topics include: population dynamics and ecology; models of infectious diseases; population genetics and evolution; biological motion (reaction-diffusion and chemotaxis); Molecular and cellular biology (biochemical kinetics, metabolic pathways, immunology). The course will introduce students to the basic mathematical concepts and techniques of dynamical systems theory (equilibria, stability, bifurcations, discrete and continuous dynamics, diffusion and wave propagation, elements of system theory and control). Mathematical exposition is supplemented with introduction to computer tools and techniques (Mathematica, Matlab). Prereq: MATH 224 or MATH 228, or BIOL/EBME 300, and MATH 201. MATH 461. Introduction to Topology. 3 Units. Metric spaces, topological spaces, and continuous functions. Compactness, connectedness, path connectedness. Topological manifolds; topological groups. Polyhedra, simplical complexes. Fundamental groups. Prereq: MATH 224 or MATH 228. MATH 462. Algebraic Topology. 3 Units. The fundamental group and covering spaces; van Kampen's theorem. Higher homotopy groups; long-exact sequence of a pair. Homology theory; chain complexes; short and long exact sequences; Mayer-Vietoris sequence. Homology of surfaces and complexes; applications. Prereq: MATH 461.
7 MATH (MATH) 7 MATH 465. Differential Geometry. 3 Units. Manifolds and differential geometry. Vector fields; Riemannian metrics; curvature; intrinsic and extrinsic geometry of surfaces and curves; structural equations of Riemannian geometry; the Gauss-Bonnet theorem. Prereq: MATH 321. MATH 467. Differentiable Manifolds. 3 Units. Differentiable manifolds and structures on manifolds. Tangent and cotangent bundle; vector fields; differential forms; tensor calculus; integration and Stokes' theorem. May include Hamiltonian systems and their formulation on manifolds; symplectic structures; connections and curvature; foliations and integrability. Prereq: MATH 322. MATH 471. Advanced Engineering Mathematics. 3 Units. Vector analysis, Fourier series and integrals. Laplace transforms, separable partial differential equations, and boundary value problems. Bessel and Legendre functions. Emphasis on techniques and applications. Prereq: MATH 224 or MATH 228. MATH 473. Introduction to Mathematical Image Processing and Computer Vision. 3 Units. This course introduces fundamental mathematics techniques for image processing and computer vision (IPCV). It is accessible to upper level undergraduate and graduate students from mathematics, sciences, engineering and medicine. Topics include but are not limited to image denoising, contrast enhancement, image compression, image segmentation and pattern recognition. Main tools are discrete Fourier analysis and wavelets, plus some statistics, optimization and a little calculus of variation and partial differential equations if time permitting. Students gain a solid theoretical background in IPCV modeling and computing, and master hands-on application experiences. Upon completion of the course, students will have clear understanding of classical methods, which will help them develop new methodical approaches for imaging problems arising in a variety of fields. Recommended preparation: Some coursework in scientific computing and ability to program in (or willingness to learn) a language such as Matlab or C/C++. Prereq: MATH 330 or MATH 431 or equivalent. MATH 475. Mathematics of Imaging in Industry and Medicine. 3 Units. The mathematics of image reconstruction; properties of radon transform, relation to Fourier transform; inversion methods, including convolution, backprojection, rho-filtered layergram, algebraic reconstruction technique (ART), and orthogonal polynomial expansions. Reconstruction from fan beam geometry, limited angle techniques used in MRI; survey of applications. Recommended preparation: PHYS 431 or MATH 471. MATH 478. Computational Neuroscience. 3 Units. Computer simulations and mathematical analysis of neurons and neural circuits, and the computational properties of nervous systems. Students are taught a range of models for neurons and neural circuits, and are asked to implement and explore the computational and dynamic properties of these models. The course introduces students to dynamical systems theory for the analysis of neurons and neural learning, models of brain systems, and their relationship to artificial and neural networks. Term project required. Students enrolled in MATH 478 will make arrangements with the instructor to attend additional lectures and complete additional assignments addressing mathematical topics related to the course. Recommended preparation: MATH 223 and MATH 224 or BIOL 300 and BIOL 306. Offered as BIOL 378, COGS 378, MATH 378, BIOL 478, EBME 478, EECS 478, MATH 478 and NEUR 478. MATH 491. Probability I. 3 Units. Probabilistic concepts. Discrete probability, elementary distributions. Measure theoretic framework of probability theory. Probability spaces, sigma algebras, expectations, distributions. Independence. Classical results on almost sure convergence of sums of independent random variables. Kolmogorov's law of large numbers. Recurrence of sums. Weak convergence of probability measures. Inversion, Levy's continuity theorem. Central limit theorem. Introduction to the central limit problem. Prereq: MATH 322. MATH 492. Probability II. 3 Units. Conditional expectations. Discrete parameter martingales. Stopping times, optional stopping. Discrete parameter stationary processes and ergodic theory. Discrete time Markov processes. Introduction to continuous parameter stochastic processes. Kolmogorov's consistency theorem. Gaussian processes. Brownian motion theory (sample path properties, strong Markov property, Martingales associated to Brownian motion, functional central limit theorem). Prereq: MATH 491. MATH 494. Introduction to Information Theory. 3 Units. This course is intended as an introduction to information and coding theory with emphasis on the mathematical aspects. It is suitable for advanced undergraduate and graduate students in mathematics, applied mathematics, statistics, physics, computer science and electrical engineering. Course content: Information measures-entropy, relative entropy, mutual information, and their properties. Typical sets and sequences, asymptotic equipartition property, data compression. Channel coding and capacity: channel coding theorem. Differential entropy, Gaussian channel, Shannon-Nyquist theorem. Information theory inequalities (400 level). Additional topics, which may include compressed sensing and elements of quantum information theory. Recommended preparation: MATH 201 or MATH 307. Offered as MATH 394, EECS 394, MATH 494 and EECS 494. MATH 497. Stochastic Models: Time Series and Markov Chains. 3 Units. Introduction to stochastic modeling of data. Emphasis on models and statistical analysis of data with a significant temporal and/or spatial structure. This course will analyze time and space dependent random phenomena from two perspectives: Stationary Time Series: Spectral representation of deterministic signals, autocorrelation. Power spectra. Transmission of stationary signals through linear filters. Optimal filter design, signal-to-noise ratio. Gaussian signals and correlation matrices. Spectral representation and computer simulation of stationary signals. Discrete Markov Chains: Transition matrices, recurrences and the first step analysis. Steady rate. Recurrence and ergodicity, empirical averages. Long run behavior, convergence to steady state. Time to absorption. Eigenvalues and nonhomogeneous Markov chains. Introduction to Gibbs fields and Markov Chain Monte Carlo (MCMC). This course is related to STAT 538 but can be taken independently of it. Offered as: MATH 497 and STAT 437. Prereq: STAT 243/244 (as a sequence) or STAT 312 or STAT 313 or STAT 332 or STAT 333 or STAT 345 or MATH 380 or MATH 491 or Requisites Not Met permission. MATH 499. Special Topics. 3 Units. Special topics in mathematics. MATH 528. Analysis Seminar. 1-3 Units. Continuing seminar on areas of current interest in analysis. Allows graduate and advanced undergraduate students to become involved in research. Topics will reflect interests and expertise of the faculty and may include functional analysis, convexity theory, and their applications. May be taken more than once for credit. Consent of department required.
8 8 MATH (MATH) MATH 535. Applied Mathematics Seminar. 1-3 Units. Continuing seminar on areas of current interest in applied mathematics. Allows graduate and advanced undergraduate students to become involved in research. Topics will reflect interests and expertise of the faculty and may include topics in applied probability and stochastic processes, continuum mechanics, numerical analysis, mathematical physics or mathematical biology. May be taken more than once for credit. MATH 549. Mathematical Life Sciences Seminar. 1-3 Units. Continuing seminar on areas of current interest in the applications of mathematics to the life sciences. Allows graduate and advanced undergraduate students to become involved in research. Topics will reflect interests and expertise of the faculty and may include mathematical biology, computational neuroscience, mathematical modeling of biological systems, models of infectious diseases, computational cell biology, mathematical ecology and mathematical biomedicine broadly constructed. May be taken more than once for credit. MATH 598. Stochastic Models: Diffusive Phenomena and Stochastic Differential Equations. 3 Units. Introduction to stochastic modeling of data. Emphasis on models and statistical analysis of data with significant temporal and/or spatial structure. This course will analyze time and space dependent random phenomena from two perspectives: Brownian motion and diffusive processes: Classification of stochastic processes, finite dimensional distributions, random walks and their scaling limits, Brownian motion and its paths properties, general diffusive processes, Fokker-Planck- Kolmogorov equations, Poisson and point processes, heavy tail diffusions, Levy processes, tempered stable diffusions. Stochastic calculus and stochastic differential equations: Wiener random integrals, mean-square theory, Brownian stochastic integrals and Ito formula, stochastic integrals for Levy processes, martingale property, basic theory and applications of stochastic differential equations. This course is related to STAT 437 but can be taken independently of it. Offered as MATH 598 and STAT 538. MATH 601. Reading and Research Problems Units. Presentation of individual research, discussion, and investigation of research papers in a specialized field of mathematics. MATH 651. Thesis (M.S.) Units. MATH 701. Dissertation (Ph.D.). 1-9 Units. Prereq: Predoctoral research consent or advanced to Ph.D. candidacy milestone.
Mathematics (MATH) MATH 098. Intermediate Algebra. 3 Credits. MATH 103. College Algebra. 3 Credits. MATH 104. Finite Mathematics. 3 Credits.
Mathematics (MATH) 1 Mathematics (MATH) MATH 098. Intermediate Algebra. 3 Credits. Properties of the real number system, factoring, linear and quadratic equations, functions, polynomial and rational expressions,
More informationCourses: Mathematics (MATH)College: Natural Sciences & Mathematics. Any TCCN equivalents are indicated in square brackets [ ].
Courses: Mathematics (MATH)College: Natural Sciences & Mathematics Any TCCN equivalents are indicated in square brackets [ ]. MATH 1300: Fundamentals of Mathematics Cr. 3. (3-0). A survey of precollege
More informationMathematics (MATH) Courses
Mathematics (MATH) 1 Mathematics (MATH) Courses MATH A054 Prealgebra 3 Topics include operations and applications of whole numbers, integers, fractions, decimals, ratios and proportions, percents, geometry
More informationMATHEMATICS (MATH) Mathematics (MATH) 1
Mathematics (MATH) 1 MATHEMATICS (MATH) MATH F113X Numbers and Society (m) Numbers and data help us understand our society. In this course, we develop mathematical concepts and tools to understand what
More informationMATHEMATICS (MATH) Calendar
MATHEMATICS (MATH) This is a list of the Mathematics (MATH) courses available at KPU. For information about transfer of credit amongst institutions in B.C. and to see how individual courses transfer, go
More informationMATHEMATICS (MATH) Mathematics (MATH) 1
Mathematics (MATH) 1 MATHEMATICS (MATH) MATH117 Introductory Calculus This course is designed to introduce basic ideas and techniques of differential calculus. Students should enter with sound precalculus
More informationMathematics (MA) Mathematics (MA) 1. MA INTRO TO REAL ANALYSIS Semester Hours: 3
Mathematics (MA) 1 Mathematics (MA) MA 502 - INTRO TO REAL ANALYSIS Individualized special projects in mathematics and its applications for inquisitive and wellprepared senior level undergraduate students.
More informationMATHEMATICS (MAT) Mathematics (MAT) 1
MATHEMATICS (MAT) MAT 097 BASIC MATHEMATICS 0, 3/0 Provides the necessary mathematics background needed to pass college-level algebra; covers polynomials, rational expressions, exponents and roots, solving
More informationMATHEMATICS (MATH) Mathematics (MATH) 1 MATH AP/OTH CREDIT CALCULUS II MATH SINGLE VARIABLE CALCULUS I
Mathematics (MATH) 1 MATHEMATICS (MATH) MATH 101 - SINGLE VARIABLE CALCULUS I Short Title: SINGLE VARIABLE CALCULUS I Description: Limits, continuity, differentiation, integration, and the Fundamental
More informationMATHEMATICS (MTH) Mathematics (MTH) 1
Mathematics (MTH) 1 MATHEMATICS (MTH) MTH 099. Intermediate Algebra. 3 Credit Hours. Real number operations, polynomials, factoring, rational numbers and rational expressions. Cannot be used to fulfill
More informationMATHEMATICS (MATH) Mathematics (MATH) 1
Mathematics (MATH) 1 MATHEMATICS (MATH) MATH 1010 Applied Business Mathematics Mathematics used in solving business problems related to simple and compound interest, annuities, payroll, taxes, promissory
More informationPMATH 300s P U R E M A T H E M A T I C S. Notes
P U R E M A T H E M A T I C S Notes 1. In some areas, the Department of Pure Mathematics offers two distinct streams of courses, one for students in a Pure Mathematics major plan, and another for students
More informationMATHEMATICS (MAT) Mathematics (MAT) 1
MATHEMATICS (MAT) MAT 097 BASIC MATHEMATICS 0, 3/0 Provides the necessary mathematics background needed to pass college-level algebra; covers polynomials, rational expressions, exponents and roots, solving
More informationUNIVERSITY OF SOUTH ALABAMA MATHEMATICS
UNIVERSITY OF SOUTH ALABAMA MATHEMATICS 1 Mathematics MA 105 Algebra for Math Placement 4 cr Introduction to equations of straight lines in various forms and transition between these forms; Manipulation
More informationM E M O R A N D U M. Faculty Senate approved November 1, 2018
M E M O R A N D U M Faculty Senate approved November 1, 2018 TO: FROM: Deans and Chairs Becky Bitter, Sr. Assistant Registrar DATE: October 23, 2018 SUBJECT: Minor Change Bulletin No. 5 The courses listed
More informationMATHEMATICS. Course Syllabus. Section A: Linear Algebra. Subject Code: MA. Course Structure. Ordinary Differential Equations
MATHEMATICS Subject Code: MA Course Structure Sections/Units Section A Section B Section C Linear Algebra Complex Analysis Real Analysis Topics Section D Section E Section F Section G Section H Section
More informationMA3025 Course Prerequisites
MA3025 Course Prerequisites MA 3025 (4-1) MA3025 (4-1) Logic and Discrete Mathematics: Provides a rigorous foundation in logic and elementary discrete mathematics. Topics from logic include modeling English
More informationMATHEMATICS (MATH) Mathematics (MATH) 1. MATH 802T Functions, Algebra, and Geometry for Middle Level Teachers
Mathematics (MATH) 1 MATHEMATICS (MATH) MATH 800P Number and Operation for K-3 Mathematics Specialists Description: Number and operations. Place value and its role in arithmetic operations. Development
More informationMathematics 0005 Intermediate Algebra (3) 1020 Contemporary Mathematics (3) 1030 College Algebra (3) 1035 Trigonometry (2) .
Mathematics 0005 Intermediate Algebra (3) Prerequisite: A satisfactory score on the university s mathematics placement examination, obtained in the six months prior to enrollment in this course. Preparatory
More informationCourse Description - Master in of Mathematics Comprehensive exam& Thesis Tracks
Course Description - Master in of Mathematics Comprehensive exam& Thesis Tracks 1309701 Theory of ordinary differential equations Review of ODEs, existence and uniqueness of solutions for ODEs, existence
More informationDepartment of Mathematics
Department of Mathematics FACULTY Professors Jungck, McAsey (chair), Szeto, Timm; Associate Professors Bedenikovic, Delgado, Hahn, Kasube, Mou, Nanyes, Quigg, Xue; Assistant Professors Haverhals, Lang;
More information3 Credits. Prerequisite: MATH 402 or MATH 404 Cross-Listed. 3 Credits. Cross-Listed. 3 Credits. Cross-Listed. 3 Credits. Prerequisite: MATH 507
Mathematics (MATH) 1 MATHEMATICS (MATH) MATH 501: Real Analysis Legesgue measure theory. Measurable sets and measurable functions. Legesgue integration, convergence theorems. Lp spaces. Decomposition and
More informationM A T H E M A T I C S
M A T H E M A T I C S Coursework Details (2018 19) Requirement : MPhil students: 2 compulsory + 3 elective courses; and PhD students: 2 compulsory + 4 elective courses (For students enrolled before January
More informationMATHEMATICS (MAT) Professors William Harris and Homer White (Chair); Visiting Assistant Professor Jianning Su; Visiting Lecturer Lucas Garnett
MATHEMATICS (MAT) Professors William Harris and Homer White (Chair); Visiting Assistant Professor Jianning Su; Visiting Lecturer Lucas Garnett The various disciplines within the Department of Mathematics,
More informationCollege of Arts and Sciences. Mathematics
108R INTERMEDIATE ALGEBRA. (3) This course is remedial in nature and covers material commonly found in second year high school algebra. Specific topics to be discussed include numbers, fractions, algebraic
More informationMATH 102 Calculus II (4-0-4)
MATH 101 Calculus I (4-0-4) (Old 101) Limits and continuity of functions of a single variable. Differentiability. Techniques of differentiation. Implicit differentiation. Local extrema, first and second
More informationMATHEMATICS (MATH) Mathematics (MATH) 1
Mathematics (MATH) 1 MATHEMATICS (MATH) MATH 500 Applied Analysis I Measure Theory and Lebesgue Integration; Metric Spaces and Contraction Mapping Theorem, Normed Spaces; Banach Spaces; Hilbert Spaces.
More informationSyllabuses for Honor Courses. Algebra I & II
Syllabuses for Honor Courses Algebra I & II Algebra is a fundamental part of the language of mathematics. Algebraic methods are used in all areas of mathematics. We will fully develop all the key concepts.
More informationMA 221 Differential Equations and Matrix Algebra I 4R-0L-4C F,W Pre: MA 113
MATHEMATICS Professors Broughton, Bryan, Carlson, Evans, Finn, Franklin, Graves, Grimaldi, Holden, Langley, Lautzenheiser, Leader, Leise, Lopez, Muir, Rader, Rickert, Sherman, and Shibberu MA 101 Introductory
More informationCOURSE DESCRIPTIONS. 1 of 5 8/21/2008 3:15 PM. (S) = Spring and (F) = Fall. All courses are 3 semester hours, unless otherwise noted.
1 of 5 8/21/2008 3:15 PM COURSE DESCRIPTIONS (S) = Spring and (F) = Fall All courses are 3 semester hours, unless otherwise noted. INTRODUCTORY COURSES: CAAM 210 (BOTH) INTRODUCTION TO ENGINEERING COMPUTATION
More informationAS 1 Math Structure for BSc (Ed) (Primary 2 CS Track) AS 1 Math Structure for BSc (Ed) (Secondary)
ACADEMIC SUBJECT: MATHEMATICS Table 1: AS 1 Math Structure for BSc (Ed) (Primary 2 CS Track) AS 1 Math Structure for BSc (Ed) (Secondary) Year 1 2 3 4 Course Code Title Course Category No. of AUs Prerequisites
More informationCourse Descriptions. Mathematics LA 848, (406)
Course Descriptions Mathematics LA 848, (406) 657-2228 M 065 Prealgebra [formerly M 061 Basic Mathematics] 3 cr. Covers pre-algebra concepts involving terminology, fractions, decimals, percent, ratio and
More informationComputational Biology Course Descriptions 12-14
Computational Biology Course Descriptions 12-14 Course Number and Title INTRODUCTORY COURSES BIO 311C: Introductory Biology I BIO 311D: Introductory Biology II BIO 325: Genetics CH 301: Principles of Chemistry
More informationGRADUATE MATHEMATICS COURSES, FALL 2018
GRADUATE MATHEMATICS COURSES, FALL 2018 Math 5043: Introduction to Numerical Analysis MW 9:00 10:20 Prof. D. Szyld During the first semester of this course, the student is introduced to basic concepts
More informationMathematics Courses (MATH)
Mathematics Courses (MATH) 1 Mathematics Courses (MATH) This is a list of all mathematics courses. For more information, see Mathematics. MATH:0100 Basic Algebra I Percents, ratio and proportion, algebraic
More informationFaculty with Research Interests For information regarding faculty visit the Department of Applied Mathematics website.
Applied Mathematics 1 APPLIED MATHEMATICS John T. Rettaliata Engineering Center, Suite 208 10 W. 32nd St. Chicago, IL 60616 312.567.8980 amath@iit.edu science.iit.edu/applied-mathematics Chair Chun Liu
More informationMathematics (MATH) Courses. Mathematics (MATH) 1
Mathematics (MATH) 1 Mathematics (MATH) Courses MATH 5000. Special Topics in Math. 3 Credit Hours. MATH 5001. Linear Algebra. 3 Credit Hours. Vector spaces and subspaces over the real and complex numbers;
More informationMATHEMATICS (MATH) Explanation of Course Numbers
MATHEMATICS (MATH) Explanation of Course Numbers Courses in the 1000s are primarily introductory undergraduate courses Those in the 2000s to 4000s are upper-division undergraduate courses that can also
More informationAPPLIED MATH (APPM) Courses. Applied Math (APPM) 1
Applied Math (APPM) 1 APPLIED MATH (APPM) Courses APPM 1235 (4) Pre-Calculus for Engineers Prepares students for the challenging content and pace of the calculus sequence required for all engineering majors.
More informationMathematics (MAT) MAT 051 Pre-Algebra. 4 Hours. Prerequisites: None. 4 hours weekly (4-0)
Mathematics (MAT) MAT 051 Pre-Algebra 4 Hours Prerequisites: None 4 hours weekly (4-0) MAT 051 is designed as a review of the basic operations of arithmetic and an introduction to algebra. The student
More informationDOCTOR OF PHILOSOPHY IN MATHEMATICS
DOCTOR OF PHILOSOPHY IN MATHEMATICS Introduction The country's science and technology capability must be developed to a level where it can contribute to the realization of our vision for the Philippines
More informationCourse Contents. Prerequisite : MATH 140
Course Contents MATH 140 : Introduction to Mathematics (E) 2 (2+0+0) credit hours Linear equations and applications, linear inequalities, absolute value in equations and inequalities, complex numbers,
More informationApplied Mathematics and Statistics Graduate Course Offerings
Applied Mathematics and Statistics Graduate Course Offerings MATH500. LINEAR VECTOR SPACES. 3.0 Semester Hrs. Finite dimensional vector spaces and subspaces: dimension, dual bases, annihilators. Linear
More informationVector fields and phase flows in the plane. Geometric and algebraic properties of linear systems. Existence, uniqueness, and continuity
Math Courses Approved for MSME (2015/16) Mth 511 - Introduction to Real Analysis I (3) elements of functional analysis. This is the first course in a sequence of three: Mth 511, Mth 512 and Mth 513 which
More informationMathematics (MTH) Mathematics (MTH) 1
Mathematics (MTH) 1 Mathematics (MTH) Note: 1. Service courses do not count toward majors in the Department of Mathematics. They may or may not count toward majors in other departments. Look carefully
More informationSTUDY PLAN MASTER IN (MATHEMATICS) (Thesis Track)
STUDY PLAN MASTER IN (MATHEMATICS) (Thesis Track) I. GENERAL RULES AND CONDITIONS: 1- This plan conforms to the regulations of the general frame of the Master programs. 2- Areas of specialty of admission
More informationPMATH 600s. Prerequisite: PMATH 345 or 346 or consent of department.
PMATH 600s PMATH 632 First Order Logic and Computability (0.50) LEC Course ID: 002339 The concepts of formal provability and logical consequence in first order logic are introduced, and their equivalence
More informationMATHEMATICS (MA) Mathematics (MA) 1
Mathematics (MA) 1 MATHEMATICS (MA) MA 0010 Mathematics for Liberal Arts This course presents major mathematical concepts in an historical and cultural setting. Topics include geometry, set theory and
More informationBASIC EXAM ADVANCED CALCULUS/LINEAR ALGEBRA
1 BASIC EXAM ADVANCED CALCULUS/LINEAR ALGEBRA This part of the Basic Exam covers topics at the undergraduate level, most of which might be encountered in courses here such as Math 233, 235, 425, 523, 545.
More informationCollege of Arts and Sciences. Mathematics
108R INTERMEDIATE ALGEBRA. (3) This course is remedial in nature and covers material commonly found in second year high school algebra. Specific topics to be discussed include numbers, fractions, algebraic
More informationUNIVERSITY OF NORTH ALABAMA MA 110 FINITE MATHEMATICS
MA 110 FINITE MATHEMATICS Course Description. This course is intended to give an overview of topics in finite mathematics together with their applications and is taken primarily by students who are not
More informationPrerequisite: STATS 7 or STATS 8 or AP90 or (STATS 120A and STATS 120B and STATS 120C). AP90 with a minimum score of 3
University of California, Irvine 2017-2018 1 Statistics (STATS) Courses STATS 5. Seminar in Data Science. 1 Unit. An introduction to the field of Data Science; intended for entering freshman and transfers.
More informationMA-Mathematics Courses
The University of Alabama at Birmingham 1 MA-Mathematics Courses Courses MA 094. Basic 3 Hours. Whole numbers, fractions, decimals, ratios and proportions, percentages, integers, basic geometry, and basic
More informationMaster of Science in Statistics A Proposal
1 Master of Science in Statistics A Proposal Rationale of the Program In order to cope up with the emerging complexity on the solutions of realistic problems involving several phenomena of nature it is
More informationMAT 2030 Calculus III Cr. 4. Prerequisites: MAT 2020 with a minimum grade of C- Prerequisite: MAT 2020 (may be taken concurrently) with a minimum
MAT - MATHEMATICS For details on Mathematics prerequisite requirements, please see the Mathematics Placement Information (http://bulletins.wayne.edu/ undergraduate/college-liberal-arts-sciences/mathematics/placement)
More informationCourse Contents. L space, eigen functions and eigen values of self-adjoint linear operators, orthogonal polynomials and
Course Contents MATH5101 Ordinary Differential Equations 4(3+1) Existence and uniqueness of solutions of linear systems. Stability Theory, Liapunov method. Twodimensional autonomous systems, oincare-bendixson
More informationMathematics (MATH) Courses. University of California, Irvine
University of California, Irvine 2017-2018 1 Mathematics (MATH) Courses MATH 1A. Pre-Calculus. Basic equations and inequalities, linear and quadratic functions, and systems of simultaneous equations. Grading
More informationREFERENCES Dummit and Foote, Abstract Algebra Atiyah and MacDonald, Introduction to Commutative Algebra Serre, Linear Representations of Finite
ADVANCED EXAMS ALGEBRA I. Group Theory and Representation Theory Group actions; counting with groups. p-groups and Sylow theorems. Composition series; Jordan-Holder theorem; solvable groups. Automorphisms;
More informationCourse Goals and Course Objectives, as of Fall Math 102: Intermediate Algebra
Course Goals and Course Objectives, as of Fall 2015 Math 102: Intermediate Algebra Interpret mathematical models such as formulas, graphs, tables, and schematics, and draw inferences from them. Represent
More informationPHYSICS. For Senior Comprehensives. Requirements for a Major. Physics 1
Physics 1 PHYSICS Physics is the study of the fundamental laws that govern our universe. Our curriculum is designed to give our students a solid foundation for understanding these laws and how they were
More informationIntroduction to the Mathematical and Statistical Foundations of Econometrics Herman J. Bierens Pennsylvania State University
Introduction to the Mathematical and Statistical Foundations of Econometrics 1 Herman J. Bierens Pennsylvania State University November 13, 2003 Revised: March 15, 2004 2 Contents Preface Chapter 1: Probability
More informationMATH - MATHEMATICS. MATH - Mathematics 1. Continuation of MATH410. Prerequisite: Minimum grade of C- in MATH410; and permission of
MATH - Mathematics 1 MATH - MATHEMATICS MATH401 Applications of Linear Algebra (3 Credits) Various applications of linear algebra: theory of finite games, linear programming, matrix methods as applied
More informationILLINOIS LICENSURE TESTING SYSTEM
ILLINOIS LICENSURE TESTING SYSTEM FIELD 115: MATHEMATICS November 2003 Illinois Licensure Testing System FIELD 115: MATHEMATICS November 2003 Subarea Range of Objectives I. Processes and Applications 01
More informationSyllabus for Applied Mathematics Graduate Student Qualifying Exams, Dartmouth Mathematics Department
Syllabus for Applied Mathematics Graduate Student Qualifying Exams, Dartmouth Mathematics Department Alex Barnett, Scott Pauls, Dan Rockmore August 12, 2011 We aim to touch upon many topics that a professional
More informationTrinity Christian School Curriculum Guide
Course Title: Calculus Grade Taught: Twelfth Grade Credits: 1 credit Trinity Christian School Curriculum Guide A. Course Goals: 1. To provide students with a familiarity with the properties of linear,
More informationCareer Opportunities Teaching, Consultants to actuaries, Management Services & Computing, Accountancy, Statistical Work.
Department of Mathematics and Computer Science Mathematics Program Mission The program provides students with the opportunity to study the primary areas of contemporary mathematics, provides physical and
More informationSpecial Two-Semester Linear Algebra Course (Fall 2012 and Spring 2013)
Special Two-Semester Linear Algebra Course (Fall 2012 and Spring 2013) The first semester will concentrate on basic matrix skills as described in MA 205, and the student should have one semester of calculus.
More informationSTATISTICS-STAT (STAT)
Statistics-STAT (STAT) 1 STATISTICS-STAT (STAT) Courses STAT 158 Introduction to R Programming Credit: 1 (1-0-0) Programming using the R Project for the Statistical Computing. Data objects, for loops,
More informationMATHEMATICS CERTIFICATE FACULTY COURSES UNDERGRADUATE GRADUATE. Certificate programs. Explanation of Course Numbers. Bachelor's programs.
MATHEMATICS The Department of Mathematics, part of the natural and mathematical sciences discipline in the Columbian College of Arts and Sciences, offers the bachelor of arts in mathematics and bachelor
More informationInternational Mathematical Union
International Mathematical Union To: From: IMU Adhering Organizations Major Mathematical Societies and Institutions Martin Grötschel, IMU Secretary October 24, 2007 IMU AO Circular Letter 7/2007 ICM 2010:
More informationMathematics (MATH) Lehigh University
Lehigh University 2018-2019 1 Mathematics (MATH) Courses MATH 000 Preparation for Calculus 2 Intensive review of fundamental concepts in mathematics utilized in calculus, including functions and graphs,
More informationMajor Matrix Mathematics Education 7-12 Licensure - NEW
Course Name(s) Number(s) Choose One: MATH 303Differential Equations MATH 304 Mathematical Modeling MATH 305 History and Philosophy of Mathematics MATH 405 Advanced Calculus MATH 406 Mathematical Statistics
More informationThe Way of Analysis. Robert S. Strichartz. Jones and Bartlett Publishers. Mathematics Department Cornell University Ithaca, New York
The Way of Analysis Robert S. Strichartz Mathematics Department Cornell University Ithaca, New York Jones and Bartlett Publishers Boston London Contents Preface xiii 1 Preliminaries 1 1.1 The Logic of
More informationMATHEMATICS (MATH) Mathematics (MATH) 1
Mathematics (MATH) 1 MATHEMATICS (MATH) MATH 104 Calculus, Part I Brief review of High School calculus, applications of integrals, transcendental functions, methods of integration, infinite series, Taylor's
More informationMIDLAND ISD ADVANCED PLACEMENT CURRICULUM STANDARDS AP CALCULUS BC
Curricular Requirement 1: The course teaches all topics associated with Functions, Graphs, and Limits; Derivatives; Integrals; and Polynomial Approximations and Series as delineated in the Calculus BC
More informationRandom Vibrations & Failure Analysis Sayan Gupta Indian Institute of Technology Madras
Random Vibrations & Failure Analysis Sayan Gupta Indian Institute of Technology Madras Lecture 1: Introduction Course Objectives: The focus of this course is on gaining understanding on how to make an
More informationABSTRACT ALGEBRA WITH APPLICATIONS
ABSTRACT ALGEBRA WITH APPLICATIONS IN TWO VOLUMES VOLUME I VECTOR SPACES AND GROUPS KARLHEINZ SPINDLER Darmstadt, Germany Marcel Dekker, Inc. New York Basel Hong Kong Contents f Volume I Preface v VECTOR
More informationMathematics (MATH) Mathematics (MATH) 1
Mathematics (MATH) 1 Mathematics (MATH) MATH _0110: Intermediate Algebra MATH _0110 is a preparatory course for college algebra that carries no credit towards any baccalaureate degree. However, the grade
More informationApplied Linear Algebra
Applied Linear Algebra Peter J. Olver School of Mathematics University of Minnesota Minneapolis, MN 55455 olver@math.umn.edu http://www.math.umn.edu/ olver Chehrzad Shakiban Department of Mathematics University
More informationM.PHIL. MATHEMATICS PROGRAMME New Syllabus (with effect from Academic Year) Scheme of the Programme. of Credits
I Semester II Semester M.PHIL. MATHEMATICS PROGRAMME New Syllabus (with effect from 2018 2021 Academic Year) Scheme of the Programme Subject Subject Number Exam Internal External Total Code of Duration
More informationMATHEMATICS (MATH) Courses. Mathematics (MATH) 1
Mathematics (MATH) 1 MATHEMATICS (MATH) MATH Class Schedule (https://courses.illinois.edu/schedule/default/ DEFAULT/MATH) Courses MATH 002 Introductory Algebra credit: 3 Hours. Methods of elementary algebra,
More informationMATHEMATICS (MATH) Courses. Mathematics (MATH) 1
Mathematics (MATH) 1 MATHEMATICS (MATH) MATH Class Schedule (https://courses.illinois.edu/schedule/default/ DEFAULT/MATH) Courses MATH 002 Introductory Algebra credit: 3 Hours. Methods of elementary algebra,
More information300-Level Math Courses
300-Level Math Courses Math 250: Elementary Differential Equations A differential equation is an equation relating an unknown function to one or more of its derivatives; for instance, f = f is a differential
More informationHandbook of Stochastic Methods
C. W. Gardiner Handbook of Stochastic Methods for Physics, Chemistry and the Natural Sciences Third Edition With 30 Figures Springer Contents 1. A Historical Introduction 1 1.1 Motivation I 1.2 Some Historical
More informationTopics for the Qualifying Examination
Topics for the Qualifying Examination Quantum Mechanics I and II 1. Quantum kinematics and dynamics 1.1 Postulates of Quantum Mechanics. 1.2 Configuration space vs. Hilbert space, wave function vs. state
More informationMATH 310 Course Objectives
MATH 310 Course Objectives Upon successful completion of MATH 310, the student should be able to: Apply the addition, subtraction, multiplication, and division principles to solve counting problems. Apply
More informationMathematics. Overview. Undergraduate Programs. Graduate Programs
University of California, Berkeley 1 Mathematics Overview The Department of Mathematics is generally recognized as one of the broadest, liveliest, and most distinguished departments of mathematics in the
More informationMIDLAND ISD ADVANCED PLACEMENT CURRICULUM STANDARDS AP CALCULUS AB
Curricular Requirement 1: The course teaches all topics associated with Functions, Graphs, and Limits; Derivatives; and Integrals as delineated in the Calculus AB Topic Outline in the AP Calculus Course
More informationRAJASTHAN PUBLIC SERVICE COMMISSION, AJMER
RAJASTHAN PUBLIC SERVICE COMMISSION, AJMER SYLLABUS FOR EXAMINATION FOR THE POST OF LECTURER - MATHEMATICS, (SCHOOL EDUCATION) Paper - II Part I (Senior Secondary Standard) 1 Sets, Relations and Functions
More informationADVANCED ENGINEERING MATHEMATICS
ADVANCED ENGINEERING MATHEMATICS DENNIS G. ZILL Loyola Marymount University MICHAEL R. CULLEN Loyola Marymount University PWS-KENT O I^7 3 PUBLISHING COMPANY E 9 U Boston CONTENTS Preface xiii Parti ORDINARY
More informationADVANCED ENGINEERING MATHEMATICS MATLAB
ADVANCED ENGINEERING MATHEMATICS WITH MATLAB THIRD EDITION Dean G. Duffy Contents Dedication Contents Acknowledgments Author Introduction List of Definitions Chapter 1: Complex Variables 1.1 Complex Numbers
More informationEASTERN OREGON UNIVERSITY Chemistry-Biochemistry
EASTERN OREGON UNIVERSITY Chemistry-Biochemistry PROGRAM OBJECTIVES The chemistry-biochemistry degree offered by the Department of Chemistry-Biochemistry prepares chemistry majors for graduate work in
More informationContents. Preface to the Third Edition (2007) Preface to the Second Edition (1992) Preface to the First Edition (1985) License and Legal Information
Contents Preface to the Third Edition (2007) Preface to the Second Edition (1992) Preface to the First Edition (1985) License and Legal Information xi xiv xvii xix 1 Preliminaries 1 1.0 Introduction.............................
More informationUpon successful completion of MATH 220, the student will be able to:
MATH 220 Matrices Upon successful completion of MATH 220, the student will be able to: 1. Identify a system of linear equations (or linear system) and describe its solution set 2. Write down the coefficient
More informationMATHEMATICS. Programs. Courses. Student Learning Goals and Objectives. Mathematics 1
Mathematics 1 MATHEMATICS The mission of the Mathematics Program at Fairfield University is twofold: We strive, as mentors and teachers, to graduate majors with broad knowledge of the principal content
More informationCOWLEY COLLEGE & Area Vocational Technical School
COWLEY COLLEGE & Area Vocational Technical School COURSE PROCEDURE FOR CALCULUS I MTH4435 5 Credit Hours Student Level: This course is open to students on the college level in the freshman and/or sophomore
More informationCOMP. & APPLIED MATHEMATICS (CAAM)
Comp. & Applied Mathematics (CAAM) 1 COMP. & APPLIED MATHEMATICS (CAAM) CAAM 210 - INTRODUCTION TO ENGINEERING COMPUTATION Short Title: INTRO TO ENG COMPUTATION /Laboratory Distribution Group: Distribution
More informationCONTENTS. Preface List of Symbols and Notation
CONTENTS Preface List of Symbols and Notation xi xv 1 Introduction and Review 1 1.1 Deterministic and Stochastic Models 1 1.2 What is a Stochastic Process? 5 1.3 Monte Carlo Simulation 10 1.4 Conditional
More informationIntroduction to Mathematical Physics
Introduction to Mathematical Physics Methods and Concepts Second Edition Chun Wa Wong Department of Physics and Astronomy University of California Los Angeles OXFORD UNIVERSITY PRESS Contents 1 Vectors
More information132E Calculus I Workshop for the Emerging Scholars Program. Enrichment topics in Calculus I for students in the Emerging Scholars Program.
MATHEMATICS Department of Mathematics College of Natural Science MTH 1005 Fundamentals of Algebra Summer. 1(1-0) Factoring. Rational and exponential expressions. Linear and quadratic relations. Fractions
More information